627,760

2⁴ × 5 × 7 × 19 × 59

Starting at 627,760, the Collatz iteration reaches 1 after 110 steps. The first transition is 313880; the starting value is even with 80 positive divisors.

Prime Factor Structure

Factorization String 2^4 × 5 × 7 × 19 × 59

Distinct Prime Factors 5

Square Status No

Abundance Measure Abundant

Analytical Properties

Total Divisors 80

Divisor Sum (σ) 1,785,600

Proper Divisor Sum 1,157,840

Digit Sum / Digital Root 28 (Root: 1)

Adjacent Primes #627749 ← → #627773

Radix Representation

Decimal	627760
Binary	10011001010000110000 (20 bits)
Octal	0o2312060
Hexadecimal	0x99430

Divisor Catalog (60 of 80)

1 2 4 5 7 8 10 14 16 19 20 28 35 38 40 56 59 70 76 80 95 112 118 133 140 152 190 236 266 280 295 304 380 413 472 532 560 590 665 760 826 944 1,064 1,121 1,180 1,330 1,520 1,652 2,065 2,128 2,242 2,360 2,660 3,304 4,130 4,484 4,720 5,320 5,605 6,608

Collatz Trajectory (110 steps to reach 1)

Iterative sequence n → n/2 (if even) or 3n+1 (if odd):

627,760 313,880 156,940 78,470 39,235 117,706 58,853 176,560 88,280 44,140 22,070 11,035 33,106 16,553 49,660 24,830 12,415 37,246 18,623 55,870 27,935 83,806 41,903 125,710 62,855 188,566 94,283 282,850 141,425 424,276 212,138 106,069 318,208 159,104 79,552 39,776 19,888 9,944 4,972 2,486 1,243 3,730 1,865 5,596 2,798 1,399 4,198 2,099 6,298 3,149 9,448 4,724 2,362 1,181 3,544 1,772 886 443 1,330 665

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